$//$Applies dynamic programming to compute the largest number of

$//$coins a robot can collect on an n $\backslash$times m board by starting at $(1,1)$

$//$and moving right and down from upper left to down right corner

$//$Input: Matrix C$[1..$n$,1..$m$]$ whose elements are equal to $1$ and $0$

$//$for cells with and without a coin, respectively

$//$Output: Largest number of coins the robot can bring to cell $($n$,$ m$)$

RobotCoinCollection$($C$[1..$n$,1..$m$])$

F$[1,1]$C$[1,1]$;

for j $2$ to m do

F$[1,$ j$]$F$[1,$ j $1]+$ C$[1,$ j$]$

for i $2$ to n do

F$[$i$,1]$F$[$i $1,1]+$ C$[$i$,1]$

for j $2$ to m do

F$[$i$,$ j $]$max$($F $[$i $1,$ j$],$ F$[$i$,$ j $1])+$ C$[$i$,$ j $]$

return F$[$n$,$ m$]$

Modify this algorithm so some cells on the board $($indecated by and $\text{'}$X$\text{'}$ are inaccessible for the robot.

The input should be command line arguements in the format Columns Rows $*$

$0$ indicates the cell is empty. $1$ indicates the cell has a coin in it$.$ X indicates the cell is inexcessable.

for example

$./$robotCoin $560$ X $0100100$ X $10010$ X $10000101$ X X X $010$

Should produce this output:

Board Inputed:

$0$ X $0100$

$100$ X $10$

$010$ X $10$

$000101$

X X X $010$

Coin Collecting Table:

$000000$

$111000$

$122000$

$122334$

$000344$

The optimal path with this board is: $4$